Imagine an infinitely large sheet of square dotty paper on which you can draw triangles of any size you wish (providing each vertex is on a dot). What areas is it/is it not possible to draw?

Pinned Squares

Age 11 to 14 Challenge Level:

Pin those squares down! A geoboard is a piece of wood with pins
hammered into it. The diagram shows a 5 by 5 board with 25 pins set
out in a square array. Squares are made by stretching rubber bands
round specific pins as shown. What is the total number of squares
that can be made on a 5 by 5 board? How many squares can be made on
an N by N board?

The NRICH Project aims to enrich the mathematical experiences of all learners. To support this aim, members of the
NRICH team work in a wide range of capacities, including providing professional development for teachers wishing to
embed rich mathematical tasks into everyday classroom practice.